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main_VAR1_bootstrap.cpp
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#include <iostream>
#include <fstream>
#include <iomanip> // format manipulation
#include <string>
#include <sstream>
#include <cstdlib>
#include <math.h>
#include <cmath>
#include <numeric>
#include <stdio.h>
#include <map>
#include <unistd.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_vector.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_multimin.h>
#include <gsl/gsl_bspline.h>
#include <vector> // C++ vector class
#include <algorithm>
#include <functional>
#include <gsl/gsl_randist.h>
#include <boost/numeric/conversion/cast.hpp>
#include <boost/lexical_cast.hpp>
#include <gsl/gsl_rng.h>
#include <unistd.h>
#include <filein.h>
#include <limits>
#include <float.h>
#include <time.h>
#include <sys/time.h>
#include <chrono>
//#include <windows.h>
#include <omp.h>
#include <matrix_ops2.h>
#include <dist_corr.h>
#include <kernel.h>
#include <nl_dgp.h>
#include <dep_tests.h>
#include <plot.h>
#include <utils.h>
#include <shogun/mathematics/Math.h>
#include <shogun/mathematics/Statistics.h>
#include <shogun/lib/SGSparseVector.h>
#include <shogun/lib/config.h>
//#include <shogun/base/init.h>
//#include <shogun/base/some.h>
#include <shogun/ensemble/MajorityVote.h>
#include <shogun/evaluation/MeanSquaredError.h>
#include <shogun/labels/RegressionLabels.h>
#include <shogun/lib/SGMatrix.h>
#include <shogun/lib/SGVector.h>
#include <shogun/loss/SquaredLoss.h>
#include <shogun/machine/RandomForest.h>
#include <shogun/machine/StochasticGBMachine.h>
#include <shogun/multiclass/tree/CARTree.h>
#include <shogun/util/iterators.h>
#include <shogun/mathematics/linalg/LinalgNamespace.h>
#include <shogun/mathematics/linalg/linop/MatrixOperator.h>
#include <shogun/labels/BinaryLabels.h>
#include <shogun/features/DenseFeatures.h>
#include <shogun/kernel/GaussianKernel.h>
#include <shogun/classifier/svm/LibSVM.h>
#include <shogun/lib/common.h>
#include <shogun/io/SGIO.h>
#include <shogun/io/File.h>
//#include <ShogunML/ml_reg_6_1_4.h>
#include <ShogunML/data/data.h>
//#include <ShogunML/tscv.h>
//#include <ML_reg_dcorr.h>
#include <ML_dcorr.h>
#include <mgarch.h>
#include <nmsimplex.h>
#include <hsic_test.h>
#include <ML_dcorr_power.h>
#define CHUNK 1
using namespace std;
using namespace shogun;
using namespace shogun::linalg;
int main(void) {
//start the timer%%%%%
//time = ((double) clock())/((double) CLOCKS_PER_SEC);
auto time = std::chrono::high_resolution_clock::now();
auto timelast = time;
#if 0 //begin comment
/***********************************************************************************************************************************************************/
/*********************************************************** Start Calculating the Proposed Test Using Real Data *******************************************/
//Import a csv file of oil prices
ifstream oildata;
oildata.open ("./Application/oilprices_1977-1978.csv", ios::in);
if (!oildata)
return(EXIT_FAILURE);
vector<string> oildata1;
loadCSV(oildata, oildata1);
int T = oildata1.size() - 1; //Rows
Matrix X(T, 1);
for (auto i = 1; i <= T; i++)
X(i) = (hex2d(oildata1[i]) - hex2d (oildata1[i-1])) / hex2d (oildata1[i-1]);//calculate oil returns
oildata.close();
//Import a csv file of stock prices
ifstream stockdata;
stockdata.open ("./Application/stockprices_1977-1978.csv", ios::in);
if (!stockdata)
return(EXIT_FAILURE);
vector<vector<string>* > stockdata1;
loadCSV(stockdata, stockdata1);
int nC = (*stockdata1[1]).size(); //Columns
Matrix Y(T, nC);
for (auto i = 1; i <= T; ++i)
{
for (auto j = 1; j <= nC; ++j)
{
Y(i,j) = (hex2d ((*stockdata1[i])[j-1]) - hex2d ((*stockdata1[i-1])[j-1])) / hex2d ((*stockdata1[i-1])[j-1]);//calculate stock returns
}
}
for (vector<vector<string>*>::iterator p = stockdata1.begin( ); p != stockdata1.end( ); ++p)
{
delete *p;
}
stockdata.close();
//Write returns to file
ofstream returns;
string returns_filename = "./Application/returns_1977-1978.csv";
returns.open (returns_filename.c_str(), ios::out);
returns << "S&P 500" << " , " << "NYSE Composite" << " , " << "NASDAQ" << " , " << "OK WTI Oil" << endl;
for (auto i = 1; i <= T; ++i)
{
for (auto j = 1; j <= nC; ++j)
{
returns << Y(i,j) << " , ";
}
returns << X(i) << "\n";
}
returns.close();
/*ofstream returns;
string returns_filename = "./Application/returns.csv";
returns.open (returns_filename.c_str(), ios::out);
returns << "S&P 500" << " , " << "NYSE Composite" << " , " << "NASDAQ" << " , " << "OK WTI Oil Spot Price" << endl;
for (auto i = 1; i <= T; ++i)
{
for (auto j = 1; j <= nC; ++j)
{
returns << Y(i,j) << " , ";
}
returns << X(i) << "\n";
}
returns.close();*/
int lag_len = 20; //AR lag length
int lag_smooth = 20; //a bandwidth for the proposed statistic
Dgp dgp_obj;
Matrix resid_X(T-lag_len, 1), slope_X(lag_len+1, 1), Yj(T, 1), resid_Yj(T-lag_len, 1), slope_Yj(lag_len+1, 1), resid_Y(T-lag_len, nC);
double SSR = 0.;
dgp_obj.est_AR (resid_X, slope_X, SSR, X, lag_len);//fit X to an AR(lag_len) process, and obtain a sequence of residuals
for (auto j = 1; j <= nC; ++j) {
for (auto t = 1; t <= T; ++t) {
Yj(t) = Y(t, j);
}
dgp_obj.est_AR (resid_Yj, slope_Yj, SSR, Yj, lag_len);//fit Yj to an AR(lag_len) process, and obtain a sequence of residuals
for (auto t = 1; t <= T-lag_len; ++t) {
resid_Y(t, j) = resid_Yj(t);
}
}
ofstream output;
string output_filename = "./Application/file_out_T=" + std::to_string(T) + "_dy=" + std::to_string(nC) + "_lag_len=" + std::to_string(lag_len)
+ "_lag_smooth=" + std::to_string(lag_smooth) + ".txt";
output.open (output_filename.c_str(), ios::out);
output << "El Himdi & Roy's (1997) (HR) test: " << endl;
cout << "El Himdi & Roy's (1997) (HR) test: " << endl;
Dep_tests dep_obj;
int bandw = 10; //a bandwidth for El Himdi & Roy's (1997) statistic
do {
output << "bandwidth = " << bandw << ": HR = " << dep_obj.do_ElHimdiRoyTest (bandw, resid_X, resid_Y) << endl;
bandw += 2;
} while (bandw <= 30);
int TL = 2;//truncation lag for kernel regressions
double kernel_QDSum = 0., kernel_QRSum = 0., bandw_reg = pow(T, -0.6);//a bandwidth for nonparametric regressions
Dist_corr obj_dc (X,Y);
obj_dc.integrate_Kernel <bartlett_kernel> (&kernel_QDSum, &kernel_QRSum);//integrating a kernel function
output << "The proposed distance correlation (DC) test: " << endl;
cout << "The proposed distance correlation (DC) test: " << endl;
do {
output << "truncation lag = " << TL << ": DC = " << obj_dc.do_Test <bartlett_kernel,epanechnikov_kernel> (TL, lag_smooth, kernel_QRSum, bandw_reg) << endl;
TL += 1;
} while (TL <= 15);
output.close();
/*CSVReader reader("./Application/data.csv");
// Get the data from CSV File
std::vector<std::vector<std::string> > dataList = reader.getData();
// Print the content of row by row on screen
for(std::vector<std::string> vec : dataList)
{
for(std::string data : vec)
{
std::cout<<data << " , ";
}
std::cout<<std::endl;
}*/
/********************************************************** Finish Calculating the Proposed Test Using Real Data ********************************************/
/************************************************************************************************************************************************************/
#endif //end comment
/*Matrix alpha(3,1), beta(3,1), lambda(3,1), sigma(2,1);
alpha(1) = 0.01;
alpha(2) = 0.04;
alpha(3) = 0.02;
beta(1) = 0.7;
beta(2) = 0.4;
beta(3) = 0.5;
lambda(1) = 0.;
lambda(2) = -1;
lambda(3) = 0.;
sigma(1) = 1.5; // cf. Dgp::gen_MixedAR in dgp.h
sigma(2) = 1.5; // cf. Dgp::gen_MixedAR in dgp.h
int T = 50, bandW = 10;
double rho = 0.2;
Dgp dgp_obj;
Matrix X(T, 1), Y1(T, 1), Y2(T, 1), resid_X(T-2, 1), slope_X(3, 1), resid_Y1(T-2, 1), slope_Y1(3, 1), resid_Y2(T-2, 1), slope_Y2(3, 1), resid_Y(T-2, 2);
dgp_obj.gen_AR1 (X, Y1, Y2, alpha, beta, lambda, sigma, rho, 0., 525235);//draw two independent Gaussian random samples for X and Y := (Y1, Y2)
dgp_obj.gen_Resid (resid_X, slope_X, X);//estimate the d.g.p of X
dgp_obj.gen_Resid (resid_Y1, slope_Y1, Y1);//estimate the d.g.p of Y1
dgp_obj.gen_Resid (resid_Y2, slope_Y2, Y2);//estimate the d.g.p of Y2
for (auto t = 1; t <= T-2; ++t) {
resid_Y(t, 1) = resid_Y1(t);
resid_Y(t, 2) = resid_Y2(t);
}
Matrix cov(1, 2);
cov = cross_Cov (resid_X, resid_Y, 5);
cout << cov(1, 1) << " , " << cov(1, 2) << endl;*/
//Dep_tests dep_obj;
//cout << dep_obj.do_ElHimdiRoyTest (bandW, resid_X, resid_Y) << endl;//calculate El Himdi & Roy's test statistic
/*for (int t = 1; t <= T; ++t) {
Y(t,1) = Y1(t);
Y(t,2) = Y2(t);
}
Dist_corr dist_corr_obj (X,Y);
cout << dist_corr_obj.do_Test <daniell_kernel> (TL, lag_smooth, 0.5, alpha, beta, lambda, sigma, rho, 523532523) << endl;*/
//DWORD start = GetTickCount();
/*gsl_rng * r;
const gsl_rng_type * gen;//random number generator
gsl_rng_env_setup();
gen = gsl_rng_taus;
r = gsl_rng_alloc(gen);
gsl_rng_set(r, 143523);
int T, T_max, d_x, d_y, number_sampl, nblocks, bsize, bandwidth, seed;
double alpha = 1., ddep, pwr = 0.;
number_sampl = 500;
T = 50;
T_max = 500;
d_x = 4;
d_y = 4;
nblocks = 300;
bandwidth = 5;
bsize = 30;
ddep = 0.;*/
/*
Matrix alpha(3,1), beta(3,1), lambda(3,1), sigma(2,1);
alpha(1) = 0.01;
alpha(2) = 0.04;
alpha(3) = 0.02;
beta(1) = 0.7;
beta(2) = 0.4;
beta(3) = -0.5;
lambda(1) = 0.;
lambda(2) = -1;
lambda(3) = -0.8;
sigma(1) = 1.5; // cf. Dgp::gen_AR1 in dgp.h
sigma(2) = 1.5; // cf. Dgp::gen_AR1 in dgp.h
double rho = 0.2, threshold = 0.;//set threshold equal to 1.54 for zero correlation
int T = 200;
Matrix X(T, 1), Y(T, 2), Y1(T, 1), Y2(T, 1);
Dgp dgp_obj;
dgp_obj.gen_AR1 (X, Y1, Y2, alpha, beta, lambda, sigma, rho, threshold, 5353125);
for (int t = 1; t <= T; ++t) {
Y(t,1) = Y1(t);
Y(t,2) = Y2(t);
}
Dist_corr dc_obj(X, Y);
Matrix sigma1(3, 1);
sigma1(1) = 1.5;
sigma1(2) = 0.6;
sigma1(3) = 0.9;
cout << dc_obj.do_Test <daniell_kernel> (2, 10, 0.50, alpha, beta, lambda, sigma1, rho, 3512523) << endl;
*/
//#if 0 //begin comment
/******************************************* Start the Simulations for the Proposed Test ********************************************************************/
/************************************************************************************************************************************************************/
int seed = 1535;
int T = 100;
int L = 2;
int lag_smooth = 10; //set M_T = 3, 5, 7, 10, 20, and 25
double expn = 1.5;
int number_sampl = 100;
int num_B = 500;
/* Generate two independent sequences of i.i.d. standard normal random variables */
gsl_rng *r = nullptr;
const gsl_rng_type *gen; //random number generator
gsl_rng_env_setup();
gen = gsl_rng_taus;
r = gsl_rng_alloc(gen);
gsl_rng_set(r, seed);
SGMatrix<double> xi_x(num_B, T), xi_y(num_B, T);
for (auto i = 0; i < num_B; i++) {
for (auto t = 0; t < T; t++) {
xi_x(i,t) = gsl_ran_ugaussian (r);
xi_y(i,t) = gsl_ran_ugaussian (r);
}
}
gsl_rng_free (r); //free memory
/* List of hyperparameters used to train Random Forest */
int num_subsets = 1, min_subset_size = 10, tree_max_depths_list_size = 2, num_iters_list_size = 1, learning_rates_list_size = 10, \
subset_fractions_list_size = 4, num_rand_feats_list_size = L, num_bags_list_size = 2;
SGVector<int> tree_max_depths_list(tree_max_depths_list_size), num_iters_list(num_iters_list_size), \
num_rand_feats_list(num_rand_feats_list_size), num_bags_list(num_bags_list_size);
SGVector<double> learning_rates_list(learning_rates_list_size), subset_fractions_list(subset_fractions_list_size);
for (int i = 0; i < tree_max_depths_list_size; ++i)
tree_max_depths_list[i] = 4*(i+1);
tree_max_depths_list.display_vector("tree_max_depths_list");
for (int i = 0; i < num_iters_list_size; ++i)
num_iters_list[i] = i*100 + 200;
num_iters_list.display_vector("num_iters_list");
for (int i = 0; i < learning_rates_list_size; ++i)
learning_rates_list[i] = 0.01*(i+1);
learning_rates_list.display_vector("learning_rates_list");
for (int i = 0; i < subset_fractions_list_size; ++i)
subset_fractions_list[i] = 0.1*(i+1);
subset_fractions_list.display_vector("subset_fractions_list");
for (int i = 0; i < num_rand_feats_list_size; ++i)
num_rand_feats_list[i] = 2*(i+1);
num_rand_feats_list.display_vector("number of features list");
for (int i = 0; i < num_bags_list_size; ++i)
num_bags_list[i] = 20*i + 30;
num_bags_list.display_vector("number of bags list");
/* define VAR(1) parameters */
SGVector<double> theta1(4), theta2(4);
theta1[0] = 0.4;
theta1[1] = 0.1;
theta1[2] = -1.;
theta1[3] = 0.5;
theta2[0] = -1.5;
theta2[1] = 1.2;
theta2[2] = -0.9;
theta2[3] = 0.5;
const char *new_dir;
string dir_name, output_filename, size_filename, power_filename;
ofstream output, size_out, pwr_out;
Matrix bootstrap_REJF(2, 1);
output << std::fixed << std::setprecision(5);
/************************************************************ Using the Bartlett kernel ***********************************************************************/
// Creating a directory
dir_name = "./Results/ML/VAR/Bootstrap/BL/";
new_dir = dir_name.c_str();
if (mkdir(new_dir, 0777) == -1)
cerr << "Error : " << strerror(errno) << endl;
else
cout << "Directory created" << endl;
output_filename = dir_name + "file_out_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_expn=" + std::to_string(expn)
+ "_bartlett_kernel_bootstrap_var.txt";
size_filename = dir_name + "size_out_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_expn=" + std::to_string(expn)
+ "_bartlett_kernel_bootstrap_var.txt";
power_filename = dir_name + "power_out_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_expn=" + std::to_string(expn)
+ "_bartlett_kernel_bootstrap_var.txt";
output.open (output_filename.c_str(), ios::out);
size_out.open (size_filename.c_str(), ios::out);
pwr_out.open (power_filename.c_str(), ios::out);
output << "Lag smooth length = " << lag_smooth << endl;
//calculate 5%- and 10%- empirical sizes
int choose_alt = 0;
ML_dcorr_power::power_f<NL_Dgp::gen_VAR, ML_DCORR::do_Test_bt<ML_REG::RF_cv1, ML_REG::RF_Plot, bartlett_kernel>> \
( bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta1, theta2, /*true parameters of two DGPs*/
number_sampl, /*number of random samples drawn*/
L, /*maximum truncation lag*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
num_subsets, /*number of subsets for TSCV*/
min_subset_size, /*minimum subset size for TSCV*/
tree_max_depths_list, /*list of tree max depths (for GBM)*/
num_iters_list, /*list of numbers of iterations (for GBM)*/
learning_rates_list, /*list of learning rates (for GBM)*/
subset_fractions_list, /*list of subset fractions (for GBM)*/
num_rand_feats_list, /*list of numbers of random features used for bagging (for RF)*/
num_bags_list, /*list of number of bags (for RF)*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5% - and 10% - sizes for the lag_smooth = " << lag_smooth << ": (" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5% - and 10% - sizes for the lag_smooth = " << lag_smooth << ": (" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
choose_alt = 1; //correlation (between eta1 and eta2) = 0.3
ML_dcorr_power::power_f<NL_Dgp::gen_VAR, ML_DCORR::do_Test_bt<ML_REG::RF_cv1, ML_REG::RF_Plot, bartlett_kernel>> \
( bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta1, theta2, /*true parameters of two DGPs*/
number_sampl, /*number of random samples drawn*/
L, /*maximum truncation lag*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
num_subsets, /*number of subsets for TSCV*/
min_subset_size, /*minimum subset size for TSCV*/
tree_max_depths_list, /*list of tree max depths (for GBM)*/
num_iters_list, /*list of numbers of iterations (for GBM)*/
learning_rates_list, /*list of learning rates (for GBM)*/
subset_fractions_list, /*list of subset fractions (for GBM)*/
num_rand_feats_list, /*list of numbers of random features used for bagging (for RF)*/
num_bags_list, /*list of number of bags (for RF)*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
choose_alt = 2; //the errors (eta1 and eta2) are not correlated, but dependent
ML_dcorr_power::power_f<NL_Dgp::gen_VAR, ML_DCORR::do_Test_bt<ML_REG::RF_cv1, ML_REG::RF_Plot, bartlett_kernel>> \
( bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta1, theta2, /*true parameters of two DGPs*/
number_sampl, /*number of random samples drawn*/
L, /*maximum truncation lag*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
num_subsets, /*number of subsets for TSCV*/
min_subset_size, /*minimum subset size for TSCV*/
tree_max_depths_list, /*list of tree max depths (for GBM)*/
num_iters_list, /*list of numbers of iterations (for GBM)*/
learning_rates_list, /*list of learning rates (for GBM)*/
subset_fractions_list, /*list of subset fractions (for GBM)*/
num_rand_feats_list, /*list of numbers of random features used for bagging (for RF)*/
num_bags_list, /*list of number of bags (for RF)*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
choose_alt = 3; //the errors (eta1 and eta2) are not correlated, but dependent
ML_dcorr_power::power_f<NL_Dgp::gen_VAR, ML_DCORR::do_Test_bt<ML_REG::RF_cv1, ML_REG::RF_Plot, bartlett_kernel>> \
( bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta1, theta2, /*true parameters of two DGPs*/
number_sampl, /*number of random samples drawn*/
L, /*maximum truncation lag*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
num_subsets, /*number of subsets for TSCV*/
min_subset_size, /*minimum subset size for TSCV*/
tree_max_depths_list, /*list of tree max depths (for GBM)*/
num_iters_list, /*list of numbers of iterations (for GBM)*/
learning_rates_list, /*list of learning rates (for GBM)*/
subset_fractions_list, /*list of subset fractions (for GBM)*/
num_rand_feats_list, /*list of numbers of random features used for bagging (for RF)*/
num_bags_list, /*list of number of bags (for RF)*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
choose_alt = 4; //the errors (eta1 and eta2) are not correlated, but dependent
ML_dcorr_power::power_f<NL_Dgp::gen_VAR, ML_DCORR::do_Test_bt<ML_REG::RF_cv1, ML_REG::RF_Plot, bartlett_kernel>> \
( bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta1, theta2, /*true parameters of two DGPs*/
number_sampl, /*number of random samples drawn*/
L, /*maximum truncation lag*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
num_subsets, /*number of subsets for TSCV*/
min_subset_size, /*minimum subset size for TSCV*/
tree_max_depths_list, /*list of tree max depths (for GBM)*/
num_iters_list, /*list of numbers of iterations (for GBM)*/
learning_rates_list, /*list of learning rates (for GBM)*/
subset_fractions_list, /*list of subset fractions (for GBM)*/
num_rand_feats_list, /*list of numbers of random features used for bagging (for RF)*/
num_bags_list, /*list of number of bags (for RF)*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
choose_alt = 5; //the errors (eta1 and eta2) are highly correlated
ML_dcorr_power::power_f<NL_Dgp::gen_VAR, ML_DCORR::do_Test_bt<ML_REG::RF_cv1, ML_REG::RF_Plot, bartlett_kernel>> \
( bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta1, theta2, /*true parameters of two DGPs*/
number_sampl, /*number of random samples drawn*/
L, /*maximum truncation lag*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
num_subsets, /*number of subsets for TSCV*/
min_subset_size, /*minimum subset size for TSCV*/
tree_max_depths_list, /*list of tree max depths (for GBM)*/
num_iters_list, /*list of numbers of iterations (for GBM)*/
learning_rates_list, /*list of learning rates (for GBM)*/
subset_fractions_list, /*list of subset fractions (for GBM)*/
num_rand_feats_list, /*list of numbers of random features used for bagging (for RF)*/
num_bags_list, /*list of number of bags (for RF)*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
output.close();
size_out.close();
pwr_out.close();
/************************************************************ Using the Daniell kernel ***********************************************************************/
// Creating a directory
dir_name = "./Results/ML/VAR/Bootstrap/DN/";
new_dir = dir_name.c_str();
if (mkdir(new_dir, 0777) == -1)
cerr << "Error : " << strerror(errno) << endl;
else
cout << "Directory created" << endl;
output_filename = dir_name + "file_out_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_expn=" + std::to_string(expn)
+ "_daniell_kernel_bootstrap_var.txt";
size_filename = dir_name + "size_out_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_expn=" + std::to_string(expn)
+ "_daniell_kernel_bootstrap_var.txt";
power_filename = dir_name + "power_out_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_expn=" + std::to_string(expn)
+ "_daniell_kernel_bootstrap_var.txt";
output.open (output_filename.c_str(), ios::out);
size_out.open (size_filename.c_str(), ios::out);
pwr_out.open (power_filename.c_str(), ios::out);
output << "Lag smooth length = " << lag_smooth << endl;
//calculate 5%- and 10%- empirical sizes
choose_alt = 0;
ML_dcorr_power::power_f<NL_Dgp::gen_VAR, ML_DCORR::do_Test_bt<ML_REG::RF_cv1, ML_REG::RF_Plot, daniell_kernel>> \
( bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta1, theta2, /*true parameters of two DGPs*/
number_sampl, /*number of random samples drawn*/
L, /*maximum truncation lag*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
num_subsets, /*number of subsets for TSCV*/
min_subset_size, /*minimum subset size for TSCV*/
tree_max_depths_list, /*list of tree max depths (for GBM)*/
num_iters_list, /*list of numbers of iterations (for GBM)*/
learning_rates_list, /*list of learning rates (for GBM)*/
subset_fractions_list, /*list of subset fractions (for GBM)*/
num_rand_feats_list, /*list of numbers of random features used for bagging (for RF)*/
num_bags_list, /*list of number of bags (for RF)*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5% - and 10% - sizes for the lag_smooth = " << lag_smooth << ": (" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5% - and 10% - sizes for the lag_smooth = " << lag_smooth << ": (" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
choose_alt = 1; //correlation (between eta1 and eta2) = 0.3
ML_dcorr_power::power_f<NL_Dgp::gen_VAR, ML_DCORR::do_Test_bt<ML_REG::RF_cv1, ML_REG::RF_Plot, daniell_kernel>> \
( bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta1, theta2, /*true parameters of two DGPs*/
number_sampl, /*number of random samples drawn*/
L, /*maximum truncation lag*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
num_subsets, /*number of subsets for TSCV*/
min_subset_size, /*minimum subset size for TSCV*/
tree_max_depths_list, /*list of tree max depths (for GBM)*/
num_iters_list, /*list of numbers of iterations (for GBM)*/
learning_rates_list, /*list of learning rates (for GBM)*/
subset_fractions_list, /*list of subset fractions (for GBM)*/
num_rand_feats_list, /*list of numbers of random features used for bagging (for RF)*/
num_bags_list, /*list of number of bags (for RF)*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
choose_alt = 2; //the errors (eta1 and eta2) are not correlated, but dependent
ML_dcorr_power::power_f<NL_Dgp::gen_VAR, ML_DCORR::do_Test_bt<ML_REG::RF_cv1, ML_REG::RF_Plot, daniell_kernel>> \
( bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta1, theta2, /*true parameters of two DGPs*/
number_sampl, /*number of random samples drawn*/
L, /*maximum truncation lag*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
num_subsets, /*number of subsets for TSCV*/
min_subset_size, /*minimum subset size for TSCV*/
tree_max_depths_list, /*list of tree max depths (for GBM)*/
num_iters_list, /*list of numbers of iterations (for GBM)*/
learning_rates_list, /*list of learning rates (for GBM)*/
subset_fractions_list, /*list of subset fractions (for GBM)*/
num_rand_feats_list, /*list of numbers of random features used for bagging (for RF)*/
num_bags_list, /*list of number of bags (for RF)*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
choose_alt = 3; //the errors (eta1 and eta2) are not correlated, but dependent
ML_dcorr_power::power_f<NL_Dgp::gen_VAR, ML_DCORR::do_Test_bt<ML_REG::RF_cv1, ML_REG::RF_Plot, daniell_kernel>> \
( bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta1, theta2, /*true parameters of two DGPs*/
number_sampl, /*number of random samples drawn*/
L, /*maximum truncation lag*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
num_subsets, /*number of subsets for TSCV*/
min_subset_size, /*minimum subset size for TSCV*/
tree_max_depths_list, /*list of tree max depths (for GBM)*/
num_iters_list, /*list of numbers of iterations (for GBM)*/
learning_rates_list, /*list of learning rates (for GBM)*/
subset_fractions_list, /*list of subset fractions (for GBM)*/
num_rand_feats_list, /*list of numbers of random features used for bagging (for RF)*/
num_bags_list, /*list of number of bags (for RF)*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
choose_alt = 4; //the errors (eta1 and eta2) are not correlated, but dependent
ML_dcorr_power::power_f<NL_Dgp::gen_VAR, ML_DCORR::do_Test_bt<ML_REG::RF_cv1, ML_REG::RF_Plot, daniell_kernel>> \
( bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta1, theta2, /*true parameters of two DGPs*/
number_sampl, /*number of random samples drawn*/
L, /*maximum truncation lag*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
num_subsets, /*number of subsets for TSCV*/
min_subset_size, /*minimum subset size for TSCV*/
tree_max_depths_list, /*list of tree max depths (for GBM)*/
num_iters_list, /*list of numbers of iterations (for GBM)*/
learning_rates_list, /*list of learning rates (for GBM)*/
subset_fractions_list, /*list of subset fractions (for GBM)*/
num_rand_feats_list, /*list of numbers of random features used for bagging (for RF)*/
num_bags_list, /*list of number of bags (for RF)*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
choose_alt = 5; //the errors (eta1 and eta2) are highly correlated
ML_dcorr_power::power_f<NL_Dgp::gen_VAR, ML_DCORR::do_Test_bt<ML_REG::RF_cv1, ML_REG::RF_Plot, daniell_kernel>> \
( bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta1, theta2, /*true parameters of two DGPs*/
number_sampl, /*number of random samples drawn*/
L, /*maximum truncation lag*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
num_subsets, /*number of subsets for TSCV*/
min_subset_size, /*minimum subset size for TSCV*/
tree_max_depths_list, /*list of tree max depths (for GBM)*/
num_iters_list, /*list of numbers of iterations (for GBM)*/
learning_rates_list, /*list of learning rates (for GBM)*/
subset_fractions_list, /*list of subset fractions (for GBM)*/
num_rand_feats_list, /*list of numbers of random features used for bagging (for RF)*/
num_bags_list, /*list of number of bags (for RF)*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
output.close();
size_out.close();
pwr_out.close();
/************************************************************ Using the QS kernel ***********************************************************************/
// Creating a directory
dir_name = "./Results/ML/VAR/Bootstrap/QS/";
new_dir = dir_name.c_str();
if (mkdir(new_dir, 0777) == -1)
cerr << "Error : " << strerror(errno) << endl;
else
cout << "Directory created" << endl;
output_filename = dir_name + "file_out_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_expn=" + std::to_string(expn)
+ "_QS_kernel_bootstrap_var.txt";
size_filename = dir_name + "size_out_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_expn=" + std::to_string(expn)
+ "_QS_kernel_bootstrap_var.txt";
power_filename = dir_name + "power_out_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_expn=" + std::to_string(expn)
+ "_QS_kernel_bootstrap_var.txt";
output.open (output_filename.c_str(), ios::out);
size_out.open (size_filename.c_str(), ios::out);
pwr_out.open (power_filename.c_str(), ios::out);
output << "Lag smooth length = " << lag_smooth << endl;
//calculate 5%- and 10%- empirical sizes
choose_alt = 0;
ML_dcorr_power::power_f<NL_Dgp::gen_VAR, ML_DCORR::do_Test_bt<ML_REG::RF_cv1, ML_REG::RF_Plot, QS_kernel>> \
( bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta1, theta2, /*true parameters of two DGPs*/
number_sampl, /*number of random samples drawn*/
L, /*maximum truncation lag*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
num_subsets, /*number of subsets for TSCV*/
min_subset_size, /*minimum subset size for TSCV*/
tree_max_depths_list, /*list of tree max depths (for GBM)*/
num_iters_list, /*list of numbers of iterations (for GBM)*/
learning_rates_list, /*list of learning rates (for GBM)*/
subset_fractions_list, /*list of subset fractions (for GBM)*/
num_rand_feats_list, /*list of numbers of random features used for bagging (for RF)*/
num_bags_list, /*list of number of bags (for RF)*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5% - and 10% - sizes for the lag_smooth = " << lag_smooth << ": (" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5% - and 10% - sizes for the lag_smooth = " << lag_smooth << ": (" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
choose_alt = 1; //correlation (between eta1 and eta2) = 0.3
ML_dcorr_power::power_f<NL_Dgp::gen_VAR, ML_DCORR::do_Test_bt<ML_REG::RF_cv1, ML_REG::RF_Plot, QS_kernel>> \
( bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta1, theta2, /*true parameters of two DGPs*/
number_sampl, /*number of random samples drawn*/
L, /*maximum truncation lag*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
num_subsets, /*number of subsets for TSCV*/
min_subset_size, /*minimum subset size for TSCV*/
tree_max_depths_list, /*list of tree max depths (for GBM)*/
num_iters_list, /*list of numbers of iterations (for GBM)*/
learning_rates_list, /*list of learning rates (for GBM)*/
subset_fractions_list, /*list of subset fractions (for GBM)*/
num_rand_feats_list, /*list of numbers of random features used for bagging (for RF)*/
num_bags_list, /*list of number of bags (for RF)*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
choose_alt = 2; //the errors (eta1 and eta2) are not correlated, but dependent
ML_dcorr_power::power_f<NL_Dgp::gen_VAR, ML_DCORR::do_Test_bt<ML_REG::RF_cv1, ML_REG::RF_Plot, QS_kernel>> \
( bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta1, theta2, /*true parameters of two DGPs*/
number_sampl, /*number of random samples drawn*/
L, /*maximum truncation lag*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
num_subsets, /*number of subsets for TSCV*/
min_subset_size, /*minimum subset size for TSCV*/
tree_max_depths_list, /*list of tree max depths (for GBM)*/
num_iters_list, /*list of numbers of iterations (for GBM)*/
learning_rates_list, /*list of learning rates (for GBM)*/
subset_fractions_list, /*list of subset fractions (for GBM)*/
num_rand_feats_list, /*list of numbers of random features used for bagging (for RF)*/
num_bags_list, /*list of number of bags (for RF)*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
choose_alt = 3; //the errors (eta1 and eta2) are not correlated, but dependent
ML_dcorr_power::power_f<NL_Dgp::gen_VAR, ML_DCORR::do_Test_bt<ML_REG::RF_cv1, ML_REG::RF_Plot, QS_kernel>> \
( bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta1, theta2, /*true parameters of two DGPs*/
number_sampl, /*number of random samples drawn*/
L, /*maximum truncation lag*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
num_subsets, /*number of subsets for TSCV*/
min_subset_size, /*minimum subset size for TSCV*/
tree_max_depths_list, /*list of tree max depths (for GBM)*/
num_iters_list, /*list of numbers of iterations (for GBM)*/
learning_rates_list, /*list of learning rates (for GBM)*/
subset_fractions_list, /*list of subset fractions (for GBM)*/
num_rand_feats_list, /*list of numbers of random features used for bagging (for RF)*/
num_bags_list, /*list of number of bags (for RF)*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
choose_alt = 4; //the errors (eta1 and eta2) are not correlated, but dependent
ML_dcorr_power::power_f<NL_Dgp::gen_VAR, ML_DCORR::do_Test_bt<ML_REG::RF_cv1, ML_REG::RF_Plot, QS_kernel>> \
( bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta1, theta2, /*true parameters of two DGPs*/
number_sampl, /*number of random samples drawn*/
L, /*maximum truncation lag*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
num_subsets, /*number of subsets for TSCV*/
min_subset_size, /*minimum subset size for TSCV*/
tree_max_depths_list, /*list of tree max depths (for GBM)*/
num_iters_list, /*list of numbers of iterations (for GBM)*/
learning_rates_list, /*list of learning rates (for GBM)*/
subset_fractions_list, /*list of subset fractions (for GBM)*/
num_rand_feats_list, /*list of numbers of random features used for bagging (for RF)*/
num_bags_list, /*list of number of bags (for RF)*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
choose_alt = 5; //the errors (eta1 and eta2) are highly correlated
ML_dcorr_power::power_f<NL_Dgp::gen_VAR, ML_DCORR::do_Test_bt<ML_REG::RF_cv1, ML_REG::RF_Plot, QS_kernel>> \
( bootstrap_REJF, /*5% and 10% bootstrap rejection frequencies*/
theta1, theta2, /*true parameters of two DGPs*/
number_sampl, /*number of random samples drawn*/
L, /*maximum truncation lag*/
lag_smooth, /*kernel bandwidth*/
expn, /*exponent of the Euclidean distance*/
xi_x, xi_y, /*num_B by T matrices of auxiliary random variables used for bootstrapping*/
num_subsets, /*number of subsets for TSCV*/
min_subset_size, /*minimum subset size for TSCV*/
tree_max_depths_list, /*list of tree max depths (for GBM)*/
num_iters_list, /*list of numbers of iterations (for GBM)*/
learning_rates_list, /*list of learning rates (for GBM)*/
subset_fractions_list, /*list of subset fractions (for GBM)*/
num_rand_feats_list, /*list of numbers of random features used for bagging (for RF)*/
num_bags_list, /*list of number of bags (for RF)*/
choose_alt, /*alternative hypotheses: 1-2 (linear correlation) and 2-5 (non-correlation) as defined in Wang et al. (2021, page 22)*/
seed,
pwr_out);
output << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
cout << "5%- and 10% - empirical rejection rates for choose_alt = " << choose_alt << ": " << "(" << bootstrap_REJF(1) << " , " << bootstrap_REJF(2) << ")" << endl;
output.close();
size_out.close();
pwr_out.close();
/***************************************** Finish the Simulations for the Proposed Test *********************************************************************/
/************************************************************************************************************************************************************/
//#endif //end comment
#if 0 //begin comment
/* Calculate empirical levels of a test */
//Import a column of data
ifstream data;
data.open("e:/Dropbox/Codes/Supermicro-Office-1/Exogeneity/Results/HimdiRoy/size_out_T=200_lag_smooth=25_threshold=1.54_bivariate.txt", ios::in);
if (!data)
return(EXIT_FAILURE);
vector<string> data1;
loadCSV(data, data1);
int N = data1.size(); //Rows
Matrix X(N, 1);
for (auto i = 1; i <= N; i++)
X(i) = hex2d(data1[i-1]);
data.close();
int count10 = 0, count5 = 0;
Dep_tests dep_obj;
Matrix cv(2, 1);
int bandW = 25; //set a lag-smoothing parameter
cv = dep_obj.asymp_CV_ChiSq2 (bandW);
for (auto i = 1; i <= N; ++i) {
if (X(i) >= cv(2)) ++count10;
if (X(i) >= cv(1)) ++count5;
}
cout << "N = " << N << endl;
cout << "10% rejection rate = " << ((double) count10/N) << endl;
cout << "5% rejection rate = " << ((double) count5/N) << endl;
/*//Import a csv file
ifstream data;
data.open("./Results/Others/Correlation/QS/size_out_T=200_lag_smooth=25_rho=0.80000000000000004.txt", ios::in);
if (!data)
return(EXIT_FAILURE);
vector<vector<string>* > data1;
loadCSV(data, data1);
int nR = data1.size(); //Rows
int nC = (*data1[1]).size(); //Columns
Matrix X(nR,nC);
for (auto i = 1; i <= nR; i++)
{
for (int j = 1; j <= nC; j++)
{
X(i,j) = hex2d((*data1[i-1])[j-1]);
}
}
for (vector<vector<string>*>::iterator p = data1.begin( ); p != data1.end( ); ++p)
{
delete *p;
}
data.close();
Matrix count10(nC, 1), count5(nC, 1), asymp_cv_Haugh(2, 1);
int bandW = 25; //set a lag-smoothing parameter
Dep_tests dep_obj;
asymp_cv_Haugh = dep_obj.asymp_CV_ChiSq (bandW);
for (auto i = 1; i <= nR; ++i) {
if (X(i,1) >= 1.28) ++count10(1);
if (X(i,1) >= 1.645) ++count5(1);
if (X(i,2) >= asymp_cv_Haugh(2)) ++count10(2);
if (X(i,2) >= asymp_cv_Haugh(1)) ++count5(2);
}
cout << "N = " << nR << endl;
for (auto j = 1; j <= nC; ++j) {
cout << "Test = " << j << ": 10% rejection rate = " << ((double) count10(j)/nR) << endl;
cout << "Test = " << j << ": 5% rejection rate = " << ((double) count5(j)/nR) << endl;
}*/
#endif //end comment
#if 0 //begin comment
/************************************** Start the Simulations for the Proposed Test: The Univariate Skewed-Normal Case **************************************/
/************************************************************************************************************************************************************/
int TL = 2;
int T = 100;
int N = 1000;
int number_sampl = 500;
double expn = 1.5, delta = 0.7, rho = 0.8;
int choose_alt = 0;
unsigned long seed = 856764325;
string output_filename, size_filename, power_filename;
ofstream output, size_out, pwr_out;
int lag_smooth = 5; //set M_T = 5, 10, 20, and 25
//============================================================= Bilinear Models ===============================================================================/
Matrix asymp_CV(2,1), empir_REJF(2,1), empir_CV(2,1), asymp_REJF(2,1), alpha_X(6,1), alpha_Y(6,1), epsilon_t(N,1), epsilon_s(N,1), eta_t(N,1), eta_s(N,1);
asymp_CV(1) = 1.645; //5%-critical value from the standard normal distribution
asymp_CV(2) = 1.28; //10%-critical value from the standard normal distribution
alpha_X(1) = 0.01; //define the AR coefficients
alpha_X(2) = 0.5;
alpha_X(3) = -0.2;
alpha_X(4) = -0.1;
alpha_X(5) = 0.2;
alpha_X(6) = 0.1;
alpha_Y(1) = 0.04;
alpha_Y(2) = 0.7;
alpha_Y(3) = -0.1;
alpha_Y(4) = -0.3;
alpha_Y(5) = 0.1;
alpha_Y(6) = 0.1;
NL_Dgp::gen_RANV<NL_Dgp::gen_SN> (epsilon_t, eta_t, delta, 0., 0, 13435); //generate skewed-normal random errors
NL_Dgp::gen_RANV<NL_Dgp::gen_SN> (epsilon_s, eta_s, delta, 0., 0, 53435);
/************************************************************ Using the Bartlett kernel ***********************************************************************/
output_filename = "./Results/NonGaussian/SN/file_out_BL_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_expn="
+ std::to_string(expn) + "_bartlett_kernel_univariate.txt";
size_filename = "./Results/NonGaussian/SN/size_out_BL_T=" + std::to_string(T) + "_lag_smooth=" + std::to_string(lag_smooth) + "_expn="